Question: What will happen to all the matter that has been sucked into a black hole, after the black hole 'dies'?

Well that is a great question. As far as I know, black holes don’t die, they just keep getting bigger. Stephen Hawking proposed that they do emit particles (now known as Hawking radiation), and so are ever so slowly evaporating – but this evaporation is almost certainly totally overwhelmed by the incoming light, matter and energy that spirals in.

I don’t think anyone know what happens to the matter that has gone into a black hole. It is just trapped and no longer recognisable. Maybe Simon knows more?

I think that Matthew is basically correct. Black holes don’t die, or at least we’ve never seen any evidence that they do. Hawking radiation is a purely theoretical idea, and I don;t know if we even have a means of testing whether it’s real or not.

In astronomy we often talk about black holes “feeding” on the surrounding material, so I have a feeling that the matter that gets pulled in becomes a part of the black hole itself. That means that a black hole can grow in size and mass over time. This is the most likely answer I think, but we don’t really know for sure.